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Answer :
To solve this problem, we need to calculate the average skid mark length when a car is traveling at a speed of 57 miles per hour, with a drag factor of 1.1 and a braking efficiency of 100%.
The formula used to find the skid mark length [tex]\( s \)[/tex] is given by:
[tex]\[ s = \sqrt{30 \times D \times n} \][/tex]
where:
- [tex]\( D \)[/tex] is the speed in miles per hour (mi/h).
- [tex]\( n \)[/tex] is the drag factor (a measure of how much the road surface slows down the car).
Given:
- [tex]\( D = 57 \)[/tex] mi/h
- [tex]\( n = 1.1 \)[/tex]
- Braking efficiency is 100%, which means it doesn't change our calculation.
To find the skid mark length [tex]\( s \)[/tex]:
1. Multiply the speed [tex]\( D \)[/tex] by the drag factor [tex]\( n \)[/tex]:
[tex]\[ 57 \times 1.1 = 62.7 \][/tex]
2. Multiply the result by 30:
[tex]\[ 30 \times 62.7 = 1881 \][/tex]
3. Find the square root of the product:
[tex]\[ \sqrt{1881} \approx 43.37 \][/tex]
4. Round the result to the nearest tenth of a foot:
[tex]\[ 43.4 \text{ feet} \][/tex]
Therefore, the average skid mark length, to the nearest tenth of a foot, is [tex]\(\boxed{43.4}\)[/tex] feet.
The formula used to find the skid mark length [tex]\( s \)[/tex] is given by:
[tex]\[ s = \sqrt{30 \times D \times n} \][/tex]
where:
- [tex]\( D \)[/tex] is the speed in miles per hour (mi/h).
- [tex]\( n \)[/tex] is the drag factor (a measure of how much the road surface slows down the car).
Given:
- [tex]\( D = 57 \)[/tex] mi/h
- [tex]\( n = 1.1 \)[/tex]
- Braking efficiency is 100%, which means it doesn't change our calculation.
To find the skid mark length [tex]\( s \)[/tex]:
1. Multiply the speed [tex]\( D \)[/tex] by the drag factor [tex]\( n \)[/tex]:
[tex]\[ 57 \times 1.1 = 62.7 \][/tex]
2. Multiply the result by 30:
[tex]\[ 30 \times 62.7 = 1881 \][/tex]
3. Find the square root of the product:
[tex]\[ \sqrt{1881} \approx 43.37 \][/tex]
4. Round the result to the nearest tenth of a foot:
[tex]\[ 43.4 \text{ feet} \][/tex]
Therefore, the average skid mark length, to the nearest tenth of a foot, is [tex]\(\boxed{43.4}\)[/tex] feet.
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